This paper deals with scalarization and stability aspects for a unified set optimization problem. We provide characterization preference relation the corresponding minimal solution in terms of generalized oriented distance function sup-inf type. establish continuity associated an existence result solution. Painlevé–Kuratowski convergence solutions family scalar problems to

As it became well known in the past years, Einstein-scalar-Gauss-Bonnet (EsGB) theories evade no-hair theorems and allow for scalarized compact objects including black holes (BH). The coupling function that defines theory is main character process nature of scalarization. With right choice, becomes an extension general relativity (GR) sense any solution to GR field equations remains a EsGB theo...

We study the linear instability and nonlinear dynamical evolution of Reissner-Nordstr\"om (RN) black hole in Einstein-Maxwell-scalar theory asymptotic flat spacetime. focus on coupling function $f(\phi)=e^{-b\phi^2}$ which allows both scalar-free RN solution scalarized solution. first present system parameters during dynamic scalarization. For parameter regions where spontaneous scalarization o...

We study the process of fully nonlinear dynamical scalarization starting from a charged black hole or naked singularity in asymptotically flat spacetime Einstein-Maxwell-dilaton theory. Initially dilaton field is negligible compared to gravitational and Maxwell field. Then experiences an immediate growth, later it oscillates with damping amplitude finally settles down finite value. For hairy de...

We study scalarization of slowly rotating black holes in the Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In slow rotation approximation $a\ll1$ with parameter $a$, GB term is given by a for Schwarzschild hole, whereas CS takes linear $a$. The tachyonic instability represents onset spontaneous scalarization. use (2+1)-dimensional hyperboloidal foliation method to show considering...

We determine the power of weighted sum scalarization with respect to computation approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion approximation that is specifically tailored case its inherent trade-offs between different objectives. For problems, provide an efficient algorithm computes problem by using exact o...

We characterize the class of (possibly incomplete) preference relations over lotteries that can be represented by a compact set of (continuous) expected utility functions which preserve both indifferences and strict preferences. This finding contrasts with the representation theorem of Dubra, Maccheroni and Ok (2004) which either delivers a noncompact set of utility functions, or at least one f...

Multi-objective optimization is known as a useful mathematical model in order to investigate some real world problems with connicting objectives, arising from economics, engineering and human decision making. In this paper, a convex composite multi-objective optimization subject to a closed convex set constraint is studied. New rst-order optimality conditions of a weakly eecient solution for th...

A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version that pro...

A procedure to approximate the nondominated set for general (continuous) bi-criteria programs is proposed. The piecewise approximation is composed of quadratic curves, each of which is developed locally in a neighborhood of a nondominated point of interest and based on primal-dual relationships associated with the weighted-Tchebycheff scalarization of the original problem. The approximating qua...